export type Point = {
  x: number
  y: number
}

// distance between 2 points
function distance(p1: Point, p2: Point): number {
  return Math.sqrt(distanceSq(p1, p2))
}

// distance between 2 points squared
function distanceSq(p1: Point, p2: Point): number {
  return Math.pow(p1.x - p2.x, 2) + Math.pow(p1.y - p2.y, 2)
}

// Sistance squared from a point p to the line segment vw
function distanceToSegmentSq(p: Point, v: Point, w: Point): number {
  const l2 = distanceSq(v, w)
  if (l2 === 0) {
    return distanceSq(p, v)
  }
  let t = ((p.x - v.x) * (w.x - v.x) + (p.y - v.y) * (w.y - v.y)) / l2
  t = Math.max(0, Math.min(1, t))
  return distanceSq(p, lerp(v, w, t))
}

function lerp(a: Point, b: Point, t: number): Point {
  return { x: a.x + (b.x - a.x) * t, y: a.y + (b.y - a.y) * t }
}

// Adapted from https://seant23.wordpress.com/2010/11/12/offset-bezier-curves/
function flatness(points: readonly Point[], offset: number): number {
  const p1 = points[offset + 0]
  const p2 = points[offset + 1]
  const p3 = points[offset + 2]
  const p4 = points[offset + 3]

  let ux = 3 * p2.x - 2 * p1.x - p4.x
  ux *= ux
  let uy = 3 * p2.y - 2 * p1.y - p4.y
  uy *= uy
  let vx = 3 * p3.x - 2 * p4.x - p1.x
  vx *= vx
  let vy = 3 * p3.y - 2 * p4.y - p1.y
  vy *= vy

  if (ux < vx) {
    ux = vx
  }

  if (uy < vy) {
    uy = vy
  }

  return ux + uy
}

function getPointsOnBezierCurveWithSplitting(
  points: readonly Point[],
  offset: number,
  tolerance: number,
  newPoints?: Point[]
): Point[] {
  const outPoints = newPoints || []
  if (flatness(points, offset) < tolerance) {
    const p0 = points[offset + 0]
    if (outPoints.length) {
      const d = distance(outPoints[outPoints.length - 1], p0)
      if (d > 1) {
        outPoints.push(p0)
      }
    } else {
      outPoints.push(p0)
    }
    outPoints.push(points[offset + 3])
  } else {
    // subdivide
    const t = 0.5
    const p1 = points[offset + 0]
    const p2 = points[offset + 1]
    const p3 = points[offset + 2]
    const p4 = points[offset + 3]

    const q1 = lerp(p1, p2, t)
    const q2 = lerp(p2, p3, t)
    const q3 = lerp(p3, p4, t)

    const r1 = lerp(q1, q2, t)
    const r2 = lerp(q2, q3, t)

    const red = lerp(r1, r2, t)

    getPointsOnBezierCurveWithSplitting([p1, q1, r1, red], 0, tolerance, outPoints)
    getPointsOnBezierCurveWithSplitting([red, r2, q3, p4], 0, tolerance, outPoints)
  }
  return outPoints
}

export function simplify(points: readonly Point[], distance: number): Point[] {
  return simplifyPoints(points, 0, points.length, distance)
}

// Ramer–Douglas–Peucker algorithm
// https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm
export function simplifyPoints(
  points: readonly Point[],
  start: number,
  end: number,
  epsilon: number,
  newPoints?: Point[]
): Point[] {
  const outPoints = newPoints || []

  // find the most distance point from the endpoints
  const s = points[start]
  const e = points[end - 1]
  let maxDistSq = 0
  let maxNdx = 1
  for (let i = start + 1; i < end - 1; ++i) {
    const distSq = distanceToSegmentSq(points[i], s, e)
    if (distSq > maxDistSq) {
      maxDistSq = distSq
      maxNdx = i
    }
  }

  // if that point is too far, split
  if (Math.sqrt(maxDistSq) > epsilon) {
    simplifyPoints(points, start, maxNdx + 1, epsilon, outPoints)
    simplifyPoints(points, maxNdx, end, epsilon, outPoints)
  } else {
    if (!outPoints.length) {
      outPoints.push(s)
    }
    outPoints.push(e)
  }

  return outPoints
}

export function pointsOnBezierCurves(
  points: readonly Point[],
  tolerance: number = 0.15,
  distance?: number
): Point[] {
  const newPoints: Point[] = []
  const numSegments = (points.length - 1) / 3
  for (let i = 0; i < numSegments; i++) {
    const offset = i * 3
    getPointsOnBezierCurveWithSplitting(points, offset, tolerance, newPoints)
  }
  if (distance && distance > 0) {
    return simplifyPoints(newPoints, 0, newPoints.length, distance)
  }
  return newPoints
}
